text: The probability that fusion occurs is greatly increased compared to the classical picture, thanks to the smearing of the effective radius as the de Broglie wavelength as well as quantum tunneling through the potential barrier. To determine the rate of fusion reactions, the value of most interest is the cross section, which describes the probability that particles will fuse by giving a characteristic area of interaction.  An estimation of the fusion cross-sectional area is often broken into three pieces:
  where  is the geometric cross section,  is the barrier transparency and  is the reaction characteristics of the reaction.
   is of the order of the square of the de Broglie wavelength  where  is the reduced mass of the system and  is the center of mass energy of the system.
   can be approximated by the Gamow transparency, which has the form:  where  is the Gamow factor and comes from estimating the quantum tunneling probability through the potential barrier.
   contains all the nuclear physics of the specific reaction and takes very different values depending on the nature of the interaction. However, for most reactions, the variation of  is small compared to the variation from the Gamow factor and so is approximated by a function called the astrophysical S-factor, , which is weakly varying in energy. Putting these dependencies together, one approximation for the fusion cross section as a function of energy takes the form:
  More detailed forms of the cross-section can be derived through nuclear physics-based models and R-matrix theory.